Algebraic entropy and the space of initial values for discrete dynamical systems

A method to calculate the algebraic entropy of a mapping which can be lifted to an isomorphism of a suitable rational surfaces (the space of initial values) are presented. It is shown that the degree of the $n$th iterate of such a mapping is given by its action on the Picard group of the space of initial values. It is also shown that the degree of the $n$th iterate of every Painlev\'e equation in sakai's list is at most $O(n^2)$ and therefore its algebraic entropy is zero.Comment: 10 pages, pLatex fil

On the geometry of C^3/D_27 and del Pezzo surfaces

We clarify some aspects of the geometry of a resolution of the orbifold X = C3/D_27, the noncompact complex manifold underlying the brane quiver standard model recently proposed by Verlinde and Wijnholt. We explicitly realize a map between X and the total space of the canonical bundle over a degree 1 quasi del Pezzo surface, thus defining a desingularization of X. Our analysis relys essentially on the relationship existing between the normalizer group of D_27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient.Comment: 23 pages, 5 figures, 2 tables. JHEP style. Added references. Corrected typos. Revised introduction, results unchanged

Modifications of the endosomal compartment in peripheral blood mononuclear cells and fibroblasts from Alzheimer’s disease patients

International audienceIdentification of blood-based biomarkers of Alzheimer’s disease (AD) remains a challenge. Neuropathological studies have identified enlarged endosomes in post-mortem brains as the earliest cellular change associated to AD. Here the presence of enlarged endosomes was investigated in peripheral blood mononuclear cells from 48 biologically defined AD patients (25 with mild cognitive impairment and 23 with dementia (AD-D)), and 23 age-matched healthy controls using immunocytochemistry and confocal microscopy. The volume and number of endosomes were not significantly different between AD and controls. However, the percentage of cells containing enlarged endosomes was significantly higher in the AD-D group as compared with controls. Furthermore, endosomal volumes significantly correlated to [C11]PiB cortical index measured by positron emission tomography in the AD group, independently of the APOE genotype, but not to the levels of amyloid-beta, tau and phosphorylated tau measured in the cerebrospinal fluid. Importantly, we confirmed the presence of enlarged endosomes in fibroblasts from six unrelated AD-D patients as compared with five cognitively normal controls. This study is the first, to our knowledge, to report morphological alterations of the endosomal compartment in peripheral cells from AD patients correlated to amyloid load that will now be evaluated as a possible biomarker

Gopakumar-Vafa invariants via vanishing cycles

In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov-Witten theory and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT invariants for irreducible one-cycles. We also give a counter-example to the Kiem-Li conjectures, where our invariants match the predicted answer. Finally, we give examples where our invariant matches the expected answer in cases where the cycle is non-reduced, non-planar, or non-primitive.Comment: 63 pages, many improvements of the exposition following referee comments, final version to appear in Inventione

Towards actionable international comparisons of health system performance: expert revision of the OECD framework and quality indicators

Objective To review and update the conceptual framework, indicator content and research priorities of the Organisation for Economic Cooperation and Development's (OECD) Health Care Quality Indicators (HCQI) project, after a decade of collaborative work. Design A structured assessment was carried out using a modified Delphi approach, followed by a consensus meeting, to assess the suite of HCQI for international comparisons, agree on revisions to the original framework and set priorities for research and development. Setting International group of countries participating to OECD projects. Participants Members of the OECD HCQI expert group. Results A reference matrix, based on a revised performance framework, was used to map and assess all seventy HCQI routinely calculated by the OECD expert group. A total of 21 indicators were agreed to be excluded, due to the following concerns: (i) relevance, (ii) international comparability, particularly where heterogeneous coding practices might induce bias, (iii) feasibility, when the number of countries able to report was limited and the added value did not justify sustained effort and (iv) actionability, for indicators that were unlikely to improve on the basis of targeted policy interventions. Conclusions The revised OECD framework for HCQI represents a new milestone of a long-standing international collaboration among a group of countries committed to building common ground for performance measurement. The expert group believes that the continuation of this work is paramount to provide decision makers with a validated toolbox to directly act on quality improvement strategie

A genetic cause of Alzheimer disease: mechanistic insights from Down syndrome

Down syndrome, caused by an extra copy of chromosome 21, is associated with a greatly increased risk of early onset Alzheimer disease. It is thought that this risk is conferred by the presence of three copies of the gene encoding amyloid precursor protein (APP), an Alzheimer risk factor, although the possession of extra copies of other chromosome 21 genes may also play a role. Further study of the mechanisms underlying the development of Alzheimer disease in Down syndrome could provide insights into the mechanisms that cause dementia in the general population

Compactifications of the moduli space of plane quartics and two lines

We study the moduli space of triples (C,L₁,L₂) consisting of quartic curves C and lines L₁ and L₂. Specifically, we construct and compactify the moduli space in two ways: via geometric invariant theory (GIT) and by using the period map of certain lattice polarized K3 surfaces. The GIT construction depends on two parameters t₁ and t₂ which correspond to the choice of a linearization. For t₁=t₂=1 we describe the GIT moduli explicitly and relate it to the construction via K3 surfaces

Synaptic vesicle recycling is unaffected in the Ts65Dn mouse model of Down syndrome

Down syndrome (DS) is the most common genetic cause of intellectual disability, and arises from trisomy of human chromosome 21. Accumulating evidence from studies of both DS patient tissue and mouse models has suggested that synaptic dysfunction is a key factor in the disorder. The presence of several genes within the DS trisomy that are either directly or indirectly linked to synaptic vesicle (SV) endocytosis suggested that presynaptic dysfunction could underlie some of these synaptic defects. Therefore we determined whether SV recycling was altered in neurons from the Ts65Dn mouse, the best characterised model of DS to date. We found that SV exocytosis, the size of the SV recycling pool, clathrin-mediated endocytosis, activity-dependent bulk endocytosis and SV generation from bulk endosomes were all unaffected by the presence of the Ts65Dn trisomy. These results were obtained using battery of complementary assays employing genetically-encoded fluorescent reporters of SV cargo trafficking, and fluorescent and morphological assays of fluid-phase uptake in primary neuronal culture. The absence of presynaptic dysfunction in central nerve terminals of the Ts65Dn mouse suggests that future research should focus on the established alterations in excitatory / inhibitory balance as a potential route for future pharmacotherapy